In recent years, a silicon optical waveguide element including a core made of silicon (Si) and a cladding made of silica (SiO2) has been drawing attention. As compared to an optical waveguide including a core made of silica, the silicon optical waveguide element has an advantage that the size of an optical waveguide can be reduced because the silicon optical waveguide element has a large refractive index difference between the core and the cladding. Further, it is possible to employ, as a production process for the silicon optical waveguide element, a production process for producing a silicon large-scale integrated circuit. Thus, the silicon optical waveguide element has another advantage that production cost can be suppressed.
The silicon optical waveguide element is fabricated by using an SOI (Silicon On Insulator) substrate. More specifically, the silicon optical waveguide element is fabricated by: first forming a silicon waveguide by patterning of an Si layer of an SOI substrate by use of a lithographic technique; and then forming a silica oxide film on the silicon wave guide.
In SOI substrates, the thickness of an Si layer is often set to 220 nm. As described above, the core is formed by patterning of an Si layer of an SOI substrate. Therefore, the waveguide which serves as the core of the silicon optical waveguide element often has a thickness of 220 nm.
Further, in such a silicon optical waveguide element, the width of a waveguide is often within a range of not less than 450 nm and not more than 500 nm. In a case where the width of the waveguide is set to less than 450 nm, a side wall(s) of the waveguide tends to be rough due to a technical limitation in a lithography process. Further, in a case where the width of the waveguide is set to less than 450 nm, light leaks more out of the waveguide as the width of the waveguide is decreased. When light that largely leaks out of the waveguide propagates through the waveguide, light loss increases significantly due to roughness of the wave guide. In other words, the roughness of the side wall(s) of the waveguide significantly increases light loss of the waveguide. On the other hand, in a case where the width of the waveguide is set to larger than 500 nm, a polarization mode of light propagating through the waveguide changes with a higher probability to another polarization mode. This becomes another factor that increases light loss of the waveguide.
As described above, the length in a vertical direction (thickness direction) of the waveguide in the silicon optical waveguide element often differs from the length in a transverse direction (width direction) of the waveguide. In other words, the waveguide of the silicon optical waveguide element has a cross-sectional shape that is anisotropic between the vertical direction and the transverse direction. In the case of such an anisotropic waveguide, there occurs a difference in group refractive index between two polarization modes of light propagating through the waveguide which two polarization modes have respective electric fields oscillating in different directions, respectively. In other words, group refractive indexes of light propagating through such an anisotropic waveguide are polarization-dependent. The two polarization modes having respective electric fields oscillating in different directions, respectively, are, for example, a TE0 mode and a TM0 mode.
Further, the silicon optical waveguide element has a feature that a relative refractive index difference between the core and the cladding is large. The silicon optical waveguide element has that feature because the core is made of silicon while the cladding is made of silica. Since the relative refractive index difference between the core and the cladding is large, the group refractive index difference of light propagating through such an anisotropic waveguide becomes larger. This results in more evident polarization dependency of the group refractive index.
The group refractive index exhibits polarization dependency, because as described above, the waveguide has different lengths in the vertical direction and in the transverse direction, respectively. Accordingly, such polarization dependency is exhibited by a waveguide that is not a silicon optical waveguide element. However, since the silicon optical waveguide element has a very large refractive index difference between silicon of which the core is made and silica of which the cladding is made, the group refractive index difference between the TE0 mode and the TM0 mode becomes very large. This results in more evident polarization dependency of the group refractive index.
When an optical signal of a TE0 mode and an optical signal of a TM0 mode are propagated from one end to the other end of a waveguide in which the group refractive index of the TE0 mode is different from the group refractive index of the TM0 mode, the time of arrival at the other end is different between the TM0 mode and the TE0 mode. The occurrence of such difference in the time of arrival is known as polarization mode dispersion, and becomes a cause of deterioration in signal characteristics of an optical signal.
For example, in a case where a waveguide has a thickness of 220 nm and a width of 500 nm, the group refractive index of a TE0 mode is 4.23 and the group refractive index of a TM0 mode is 3.87. Therefore, the group refractive index difference between the TE0 mode and the TM0 mode is 0.36. This group refractive index difference causes a difference of 6 picoseconds in the time of arrival between the TE0 mode and the TM0 mode in propagation of the TE0 mode and the TM0 mode through a waveguide having a length of 5 mm. This difference of 6 picoseconds corresponds to 0.06 UI (Unit Interval) of a 10 Gbps modulated signal, and to 0.18 UI of a 30 Gbps modulated signal. Such a difference in the time of arrival increases a jitter component of an optical signal, and consequently leads to deterioration in signal characteristics.
As a technique for compensating the above-described polarization mode dispersion, Patent Literatures 1 and 2 each disclose a technique according to which a polarization rotation element is provided at a middle point of a silicon optical waveguide element. The polarization rotation element rotates a polarization plane of incident light so as to convert a TE0 mode to a TM0 mode and a TM0 mode to a TE0 mode. Patent Literature 1 uses, as the polarization rotation element, a λ/2 plate made of a crystal plate. On the other hand, Patent Literature 2 uses, as the polarization rotation element, a λ/2 plate made of a polyimide thin film.
Further, Non-patent Literature 1 discloses a polarization rotation element partially including a rib structure, as a polarization rotation element for rotating a polarization mode in silicon.